• Title/Summary/Keyword: Nonlinear operators

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UNIQUENESS OF SOLUTIONS FOR THE BOUNDARY VALUE PROBLEM OF CERTAIN NONLINEAR ELLIPTIC OPERATORS VIA p-HARMONIC BOUNDARY

  • Lee, Yong Hah
    • Communications of the Korean Mathematical Society
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    • v.32 no.4
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    • pp.1025-1031
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    • 2017
  • We prove the uniqueness of solutions for the boundary value problem of certain nonlinear elliptic operators in the setting: Given any continuous function f on the p-harmonic boundary of a complete Riemannian manifold, there exists a unique solution of certain nonlinear elliptic operators, which is a limit of a sequence of solutions of the operators with finite energy in the sense of supremum norm, on the manifold taking the same boundary value at each p-harmonic boundary as that of f.

OPTIMIZATION AND IDENTIFICATION FOR THE NONLINEAR HYPERBOLIC SYSTEMS

  • Kang, Yong-Han
    • East Asian mathematical journal
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    • v.16 no.2
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    • pp.317-330
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    • 2000
  • In this paper we consider the optimal control problem of both operators and parameters for nonlinear hyperbolic systems. For the identification problem, we show that for every value of the parameter and operators, the optimal control problem has a solution. Moreover we obtain the necessary conditions of optimality for the optimal control problem on the system.

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CONVERGENCE OF NONLINEAR SEMIGROUPS IN A HYPERBOLIC SPACE

  • Lee, Young-S.;Park, Sang-Don
    • Communications of the Korean Mathematical Society
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    • v.13 no.1
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    • pp.171-179
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    • 1998
  • In this paper, we establish Trotted-Kato type convergence theoren for nonlinear semigroups generated by coaccretive operators in a hyperbolic space.

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Fixed Point Theorems for Mixed Monotone Vector Operators with Application to Systems of Nonlinear Boundary Value Problems

  • Sadrati, Abdellatif;Aouragh, My Driss
    • Kyungpook Mathematical Journal
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    • v.61 no.3
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    • pp.613-629
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    • 2021
  • In this paper, we present and prove new existence and uniqueness fixed point theorems for vector operators having a mixed monotone property in partially ordered product Banach spaces. Our results extend and improve existing works on τ-φ-concave operators in the scalar case. As an application, we study the existence and uniqueness of positive solutions for systems of nonlinear Neumann boundary value problems.

SUBORDINATION AND SUPERORDINATION IMPLICATIONS ASSOCIATED WITH A CLASS OF NONLINEAR INTEGRAL OPERATORS

  • SEON HYE AN;NAK EUN CHO
    • Journal of Applied and Pure Mathematics
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    • v.5 no.3_4
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    • pp.223-236
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    • 2023
  • In the present paper, we investigate the subordination and superordination implications for a class of certain nonlinear integral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich-type theorem for these integral operators is also presented. Further, we extend some results given earlier as special cases of the main results presented here.

Approximation Solvability for a System of Nonlinear Variational Type Inclusions in Banach Spaces

  • Salahuddin, Salahuddin
    • Kyungpook Mathematical Journal
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    • v.59 no.1
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    • pp.101-123
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    • 2019
  • In this paper, we consider a system of nonlinear variational type inclusions involving ($H,{\varphi},{\eta}$)-monotone operators in real Banach spaces. Further, we define a proximal operator associated with an ($H,{\varphi},{\eta}$)-monotone operator and show that it is single valued and Lipschitz continuous. Using proximal point operator techniques, we prove the existence and uniqueness of a solution and suggest an iterative algorithm for the system of nonlinear variational type inclusions. Furthermore, we discuss the convergence of the iterative sequences generated by the algorithms.

THE p-LAPLACIAN OPERATORS WITH POTENTIAL TERMS

  • Chung, Soon-Yeong;Lee, Hee-Soo
    • Communications of the Korean Mathematical Society
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    • v.26 no.4
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    • pp.591-601
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    • 2011
  • In this paper, we deal with the discrete p-Laplacian operators with a potential term having the smallest nonnegative eigenvalue. Such operators are classified as its smallest eigenvalue is positive or zero. We discuss differences between them such as an existence of solutions of p-Laplacian equations on networks and properties of the energy functional. Also, we give some examples of Poisson equations which suggest a difference between linear types and nonlinear types. Finally, we study characteristics of the set of a potential those involving operator has the smallest positive eigenvalue.

ELLIPTIC SYSTEMS INVOLVING COMPETING INTERACTIONS WITH NONLINEAR DIFFUSIONS II

  • Ahn, In-Kyung
    • Communications of the Korean Mathematical Society
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    • v.12 no.4
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    • pp.869-880
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    • 1997
  • In this paper, we give sufficient conditions of certain elliptic systems involving competing iteractions with nonlinear diffusion rates. The existence of positive solution depends on the sign of the first eigenvalue of operators of Schr$\ddot{o}$dinger type. More precisely, if the sign of such operators are either both positive or both negative, then system has a positive solution. The main tool employed is the fixed point index of compact operator on positive cones.

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EXISTENCE OF THREE WEAK SOLUTIONS FOR A CLASS OF NONLINEAR OPERATORS INVOLVING p(x)-LAPLACIAN WITH MIXED BOUNDARY CONDITIONS

  • Aramaki, Junichi
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.3
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    • pp.531-551
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    • 2021
  • In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing p(x)-Laplacian. More precisely, we consider the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters.